In a wearable device such as a head-mounted display (HMD) device, estimating the position of a user's eye can allow the HMD device to display images according to where the user's eye is located and in which direction the user is looking. The user may also interact with the HMD device by using their gaze as input to command the HMD device. In order to determine the position and gaze of the user's eye, an eye-tracking system is sometimes added to the HMD device. In addition, the eye-tracking system may capture an iris image of the user eye to enable user authentication by image analysis of the iris. However, such systems can add weight, use processing power, obscure the user's field of view, or shine too much light near the user's eyes.